Spin density wave induced disordering of the vortex lattice in superconducting La${}_{2-x}$Sr${}_x$CuO${}_4$

We use small angle neutron scattering to study the superconducting vortex lattice in La${}_{2-x}$Sr${}_x$CuO${}_4$ as a function of doping and magnetic field. We show that near optimally doping the vortex lattice coordination and the superconducting coherence length $\xi$ are controlled by a van-Hove singularity crossing the Fermi level near the Brillouin zone boundary. The vortex lattice properties change dramatically as a spin-density-wave instability is approached upon underdoping. The Bragg glass paradigm provides a good description of this regime and suggests that SDW order acts as a novel source of disorder on the vortex lattice.